Content: The course is a follow-up to the basic course Linear Algebra MAT241. We teach how to solve practical problems using modern numerical methods and computers. Central concepts are convergence, stability, and complexity (how accurate the answer will be and how rapidly it is computed). Other tools include matrix factorization and orthogonalization. Algorithms covered can, among other things, be used to solve very large systems of linear equations that arise when discretizing partial differential equations, and to compute eigenvalues.
Goal: The course provides theoretical understanding of some important algorithms. The course also provides hands-on experience of implementing these algorithms as computer code and of using them to solve applied problems. Upon completion of the course the student shall have substantially better and more useful knowledge of numerical linear algebra than students who merely have taken a basic course in scientific computing. The course shall also stimulate to independent study.
Literature: Course book is Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III, SIAM, Philadelphia, ISBN 0-89871-361-7. See also Trefethen's own page, where the first chapters can be downloaded for free. Useful supplementary text on theoretical aspects of linear algebra are, for example, Föreläsningar i Matristeori av Sven Spanne, MatematikCentrum, LTH, (1994) and Matrix Analysis and Applied Linear Algebra by Carl D. Mayer. A more advanced textbook on Numerical Linear Algebra, with more mathematical rigour, is Applied Numerical Linear Algebra by James W. Demmel.